Synchronizing neighboring tiles in a high definition map

An apparatus for synchronizing neighboring tiles in an electronic map, the apparatus comprising:

• at least one memory;
• and
• at least one processor coupled to the at least one memory, the at least one processor configured to:
• overlay a factor graph on neighboring tiles of an electronic map including a first tile group and a second tile group that border one another on at least a first tile in the first tile group and a second tile in the second tile group;
• separately optimize the first tile group and the second tile group to align a road feature that crosses between the first tile group and the second tile group, wherein separately optimize comprises optimizing a conditional distribution of each boundary crossing between the first tile group and the second tile group without optimizing individual tiles within the first tile group or the second tile group;
• shift a border of the first tile group and a border of the second tile group to join the first tile and the second tile in the second tile group or the first tile group, and repeating the separately optimizing until each tile in the first tile group and the second tile group has undergone a joint optimization with a neighboring tile;
• and
• control a trajectory of an ego vehicle along the road feature.